Abstract

We apply the technique of far-field interferometry to measure the properties of
surface waves generated by two-dimensional (2D) single subwavelength slit-groove
structures on gold films. The effective surface index of refraction
nsurf measured for the surface wave propagating
over a distance of more than 12 μm is determined to
be nsurf = 1.016± 0.004, to within
experimental uncertainty close to the expected bound surface plasmon-polariton
(SPP) value for a Au/Air interface of nspp = 1.018.
We compare these measurements to finite-difference-time-domain (FDTD) numerical
simulations of the optical field transmission through these devices. We find
excellent agreement between the measurements and the simulations for
nsurf. The measurements also show that the
surface wave propagation parameter ksurf exhibits
transient behavior close to the slit, evolving smoothly from greater values
asymptotically toward kspp over the first 2–3 μm of
slit-groove distance xsg. This behavior is confirmed
by the FDTD simulations.

Left panel: Points are the measured fringe phase
φ(xsg) as a function of
slit-groove distance xsg. The straight-line fit
is φ0 =
ksurfxsg
+ φint with constant slope
ksurf and intercept
φint. Gap in the data in left and right panels of this
figure and in the left and right panels of Fig. 4 is due to defective structures in this
interval. Right panel: Fringe amplitude η0
≃ 1/2C as a function of
xsg where C is the
interference fringe contrast.

Left panel: Fringe phase difference
φ(xsg)—φ0
as a function of slit groove distance xsg.
Deviation in the near-zone from φ0 indicates that
early, transient fringe oscillation is slightly greater and approaches
φ0 asymptotically in the far-zone beyond
~ 2 μm slit-groove distance.
Right panel: Same data as shown in left panel but on an expanded scale
of slit-groove distances to emphasize the curvature in
φ(xsg)—φ0
in the near-zone.

FDTD simulations for slit-groove center-to-center distance of 3.18
μm, slit and groove widths 100 nm,
groove depth 100 nm and gold film thickness 400 nm. Map shows
|Hy|, y-components (parallel to the slit and groove long
axis) of the magnetic field amplitude in the vicinity of the input and
output surfaces.

Phase difference φ(xsg)
—φ0 as a function of
xsg, analogous to the right panel of Fig. 4 but derived from the FDTD simulation data.
Residual “high frequency” oscillations in the
phase difference, believed to be due to numeric artifacts in the FDTD
results, have been smoothed.